Finite Group Databasebeta

#3291×D83 #36280618

order21248
automorphism?
homologyAbelianization (H1) = C25 · Schur multiplier (H2) = C29

Aliases

direct product#3291×D83

Splittings

FittingC83×#3291 ⋊ C2
SylowC83 ⋊ C2×#3291

Subgroups

subgroupG/H
centerC2D42×D83
commutator, cosocleC2×C4×C83C25
FrattiniC2×C4C24×D83
FittingC83×#3291C2
socleC2×C83C2×D42
hypercenter#3291D83
hypocenterC83C2×#3291
LCSG ▷ C2×C4×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C2×C4 ◁ #3291

2682 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1328

Conjugacy classes & character table

1247 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21248, 1045782);